索末菲积分公式在圆柱坐标系和直角坐标系间的转换  

Transformation of Sommerfeld integral formula between cylindrical coordinates and Cartesian coordinates

作　　者：霍晓云[1] 雷银照[1] 

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191

出　　处：《电工电能新技术》2012年第4期1-5,23,共6页Advanced Technology of Electrical Engineering and Energy

基　　金：国家自然科学基金资助项目(50777002)

摘　　要：索末菲积分公式可用于分析电偶极子在分层媒质中产生的电磁场问题。为了研究不同坐标系下的索末菲积分公式对电磁场表达式的影响,通过坐标系的平移和旋转得到了无限大空间中电偶极子磁矢位在不同圆柱坐标系下的表达式,利用贝塞尔函数和指数函数的积分公式将磁矢位的表达式从圆柱坐标系转化到直角坐标系,在这两种坐标系中讨论了坐标系的旋转角度与磁矢位表达式的关系。通过数值算例对理论分析进行了验证。The Sommerfeld integral formula is used to solve the electromagnetic fields produced by the electric dipole in the multilayered media. In order to study the effect of the Sommerfeld integral formula in different coordinate systems on the analytical solutions of the electromagnetic fields, the magnetic vector potential of an electric dipole in an infinite space in different cylindrical coordinate systems is derived via the translation and rotation of coordinate system. Then the expression of the magnetic vector potential is transformed from the cylindrical coordinate systeminto the Cartesian coordinate system by the integral formulas of Bessel function and exponential function. Subse- quently the relationship between the expressions of the magnetic vector potential and the rotation angles of the coor- dinates are discussed. Furthermore, the numerical examples are provided to demonstrate this conclusion. The analyses in this paper are expected to be helpful to uncover the underlying mathematical meaning of the Sommerfeld integral formula and to calculate the electromagnetic field produced by the transmission line above the ground.

关 键 词：索末菲积分公式 磁矢位 圆柱坐标系 直角坐标系 

分 类 号：TM15[电气工程—电工理论与新技术]